Descartes' Diver - To paraphrase the French philosopher Rene Descartes: "I sink, therefore I am."

 

Descartes' Diver

To paraphrase the French philosopher Rene Descartes: "I sink, therefore I am."

Squeezing the sides of a plastic soda bottle changes the fluid pressure inside. Changes influid pressure affect the buoyancy of a Cartesian diver made from an eyedropper or a Bic™ pen. The diver floats, sinks, or hovers in response to pressure changes. There are two different versions to choose from here. 
 

Eyedropper Diver

• An eyedropper.
• A tall drinking glass.
• Room-temperature water.
• One 2-liter soda bottle with screw-on cap.
• Optional: Thin, flat bottle (an empty dish washing liquid or shampoo bottle, for instance).

Bic™ Pen Diver

• A Bic™ ballpoint pen with transparent plastic body.
• Pliers.
• A small lump of modeling clay the size of a pea.
• A tall drinking glass or wide-mouthed container.
• One 2-liter soda bottle with screw-on cap.
• Room-temperature water.
• Optional: Thin, flat bottle (an empty dish washing liquid or shampoo bottle, for instance).

Eyedropper Diver

(5 minutes or less)
Fill the tall drinking glass with room-temperature water. Gradually draw water into the eyedropper until the eyedropper floats in the glass with its top barely above the surface.
Fill the soda bottle almost to the top with room-temperature water. Transfer the eyedropper into the soda bottle. Be careful not to change the amount of water in the dropper while doing this. Screw the cap onto the bottle tightly.

Bic™ Pen Diver

(5 minutes or less)
Remove the ink cartridge from the pen with a pair of pliers: It will come out easily. Notice that the empty pen body is open at one end and plugged at the other. Attach a small amount of clay around the outside of the tube near the open end, without plugging the hole. This is just for weight.

You can use another bit of clay to plug the small air hole in the side of the tube, or you can leave the air hole unplugged, allowing the water to rise higher in the tube. If you like, you can also saw the tube off to a shorter length to make a smaller diver. If you shorten the tube or leave the hole open, you will need less clay to adjust the diver's buoyancy.

Test and adjust the diver by placing it open-end-down in the drinking glass or other wide-mouthed container. Add or remove clay until the diver floats with about 1/4 inch (6.25 mm) sticking out of the water.

Fill the soda bottle almost to the top with room-temperature water. Place the diver open-end-down in the almost-full bottle, and screw the cap on tightly.

Squeeze the soda bottle to make the diver sink, rise, or hover at any depth. You also want to test your diver's responses in a thin, flat bottle, such as a bottle that originally contained dishwashing liquid or shampoo. To add a little spice, you can decorate the top of the eyedropper so that it becomes a diver with a funny face, or find small, hollow, open-bottomed toy figures to use as divers. You can also decorate the bottle. Use your imagination and creativity!

The Greek philosopher Archimedes was the first person to notice that the upward force that water exerts on an object, whether floating or submerged, is equal to the weight of the volume of water that the object displaces. That is, the buoyant force is equal to the weight of the displaced water.

As you squeeze the bottle, you increase the pressure everywhere in the bottle. The higher pressure forces more water into the eyedropper, compressing the air in the eyedropper. This causes the dropper to displace less water, thus decreasing its buoyancy and causing it to sink. When you release the sides of the bottle, the pressure decreases, and the air inside the bulb expands once again. The dropper's buoyancy increases, and the diver rises. If you look carefully, you can see the level of water changing in the dropper as you vary the pressure on the bottle.

If you use a thin, flat bottle, squeezing on the wide sides of the bottle will increase the pressure inside the bottle, but squeezing on the narrow sides will cause the volume of the bottle to expand and the pressure inside to decrease. If you use such a bottle, adjust the weight or water content of a Cartesian diver so that it barely floats. When this diver reaches the bottom of the bottle, it will stay there, even when you stop squeezing on the wide sides. You must squeeze the narrow sides to drive the diver to the surface. It will then stay at the surface even when the squeezing stops.
The key to this behavior is to carefully adjust the diver initially, so that it barely floats. As the diver sinks, the pressure outside the diver increases slightly with the water's depth. This increase is in addition to the increase in pressure you cause by squeezing the bottle. When the diver reaches the bottom and you stop squeezing, the pressure resulting from the increase in depth remains and continues to compress the air bubble a little. If the diver has been carefully balanced, this small compression of the bubble will be enough to keep the diver submerged. The process reverses when you squeeze the narrow sides to raise the diver.

Since ships float, their weight must be equal to the buoyant force of the water. The weight of a ship is therefore called its displacement.

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Depth Spinner - What happens when you get off the merry-go-round?

Depth Spinner

 

What happens when you get off the merry-go-round?

Your eyes's motion detectors are fatigued when you watch a rotating spiral. When you look away, the world seems to move toward or away from you. 

 

• Cardboard.
• Glue or tape.
• Pattern disk.
• Access to a copy machine.
• Rotator (record player, portable beater, variable-speed electric drill, hand drill, etc.).
• Optional: adhesive-backed Velcro™.
• Adult help.

(15 minutes or less)

Make a copy of the pattern disk provided as a separate page, here. Cut the pattern out and mount it on a circle of cardboard with glue or tape. Attach the disk at its center to a rotator. Old phonograph players that spin at 45 or 78 rpm are great for this. Adhesive-backed Velcro™ can be used to secure the disk to a variable-speed electric drill. The drill may also be reversed.

(5 minutes or more)

Start the spiral rotating and stare at its center for about 15 seconds.

Look away from the disk and stare at a wall or a nearby person. Notice that the wall or person seems to be expanding or contracting, like he or she is rushing toward you or away from you.

If you can, try rotating the spiral in the opposite direction. Now what happens when you look up from the spinning pattern?

Your visual system is sensitive to inward and outward motion. There are nerve cells in the visual cortex that fire more when objects move outward from the center of your field of view, and others that fire more when objects move inward. When you are looking at something that is standing still, the inward and outward channels are in balance with one another; they send equally strong signals to your brain. When you stare at this moving pattern, however, one detector channel gets tired. Then, when you stare at the wall, the detector that hasn't been working sends a stronger signal to your brain than the tired one.

If, for example, the spiral seemed to be moving away from you, the wall will seem to be moving toward you when you look up. If you rotate the spiral in the other direction, so that it seems to be moving toward you, the wall will then seem to be moving away when you look up.

You can make duplicates of the depth spinner. Make many copies of the pattern disk. Cut out the copies and paste them on small cardboard backings. You can spin your disk on a pencil point or a pin, or attach a disk to a pencil eraser with a pushpin.

Next time you are near a waterfall, try staring at one point of the waterfall for a minute. Then look at a rock or another stationary object to the side of the waterfall. The solid object will seem to flow upward. This apparent motion is due to the fatigue of the channels in your visual system that detect linear upward and downward motion.

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Cylindrical Mirror - This cylindrical mirror lets you see yourself as others see you.

 

 

Cylindrical Mirror

 

This cylindrical mirror lets you see yourself as others see you.

A flat mirror will always reflect an image that is right-side up and reversed right to left. A cylindrical mirror can produce images that are flipped upside down and images that are not reversed. The image you see in a cylindrical mirror depends on the orientation of the mirror and the distance between you and the mirror. 

 

• One 81/2 x 11 inch (22 x 28 cm) sheet of aluminized Mylar™.
• 1 transparent page protector (available in stationery stores).
• Construction paper or other stiff paper backing.

(15 minutes or less)

Put the stiff paper backing behind the Mylar™ and slide them both into the transparent page protector. Bend the Mylar™ to form a portion of a cylinder. When you bend the Mylar™, be sure that the long side is parallel to the axis of the cylinder.

Hold the cylindrical mirror so that its long axis is horizontal. Curve the Mylar™ slightly and look into the mirror. Position yourself so that you can clearly see a reflection of your face. Notice how the image changes when you move closer to or farther from the mirror. When you move far enough away from the mirror, your image will flip upside down.

Wink your right eye. Which eye does the image wink? The image may wink its left eye or its right eye, depending on how far your face is from the mirror. When you are close to the mirror and your image is right-side up, the image winks its left eye. When it is upside down, the image winks its right eye. (If you have trouble deciding which eye the image is winking, have someone stand beside the mirror and do what the image does - that is, wink the same eye as the image. Then ask your partner if he or she is winking the right or left eye. If the image is upside down, your partner will have to turn upside down, too. Your partner can bend over at the waist and look at you between the legs.)

Now orient the cylindrical mirror so that its long axis is vertical. Notice how the image changes when you move closer to and farther from the mirror. Wink your right eye and notice how the image in the mirror responds. When you are close, the image will wink its left eye. When you are far away, it will wink its right eye.

You see the world because light gets into your eyes. You see these words, for example, because light reflecting from this page enters your eyes and makes an image on your retina.
When you make a visual picture of the world, you assume that the light entering your eyes has traveled in a straight line to reach you. But mirrors and other shiny objects change the path of the light, bouncing it back in an organized fashion. When you look into a mirror, you see your image because light reflecting from your face bounces off the mirror and back into your eyes. Your eyes and brain assume that the light has traveled in a straight line to reach your eyes, so you see an image of your face out there in front of or behind the mirror.


What you see in a mirror depends on how the light bounces off the mirror and into your eyes. When light hits a mirror, it bounces off in the same way that a ball would bounce off the mirror. If you threw a ball straight at a flat mirror, it would bounce straight back. If the mirror was curved so that the ball struck the surface at an angle, it would bounce away at an angle.

When you look into an ordinary flat mirror, the image of your face is right side up: Your hair is on top of your head and your chin is underneath. To reach your eyes, the light from your hair hits the mirror at a slight angle and then bounces into your eyes from above - which is why you see your hair on top and your image as right side up.

When you look into a cylindrical mirror with the axis of the mirror horizontal and with your face a foot or more away from the mirror, your image is upside down. That's because the light from your hair bounces off the curved mirror and comes to your eyes from below.

       
To make sense of the angle at which the light is entering your eyes, your eyes and brain must see the image of your face as upside down and a little bit in front of the mirror.

As everyone knows, a flat mirror reverses your right side and your left side. How does it do that? Suppose you are standing face to face with another person. If your right ear points toward the east, his or her left ear will point toward the east. Now, instead of facing another person, suppose you are facing a flat mirror with your right ear pointing to the east. The light from your right ear will bounce off the flat mirror and enter your eyes from the east. Even though your east ear is the east ear of the image, your right ear has become the left ear of the image! (Yes, this is a little mind-boggling at first reading. But once you get it, it will seem simple.)

Now look into the cylindrical mirror with its axis vertical. Stand at least a foot away from the mirror. Once again, place your right ear so that it points to the east. Light from your right ear bounces off the curved mirror and enters your eyes from the west. Light from your right ear appears to come from the right ear of the image. In this cylindrical mirror, you see yourself as others see you. You see the image of your face just a little bit in front of the mirror.

Here's a classic tricky question: "If a flat mirror reverses right and left, why doesn't it reverse up and down?"

The answer is that a flat mirror actually reverses in and out. That is, light that travels "in" to the mirror is bounced back "out" of the mirror. This reversal does not change up into down, but it does change right into left. Consider the outline of the hand below. Is it a right hand or a left hand? You cannot tell which hand it is unless you know whether the palm of the hand is facing "in" to the page or "out" of the page. So right and left depend on in and out.


This hand is either left or right, depending on which way the palm is facing.

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Curie Point - When a piece of iron gets too hot, it is no longer attracted to a magnet

 

Curie Point

 

When a piece of iron gets too hot, it is no longer attracted to a magnet. 

 

A piece of iron will ordinarily be attracted to a magnet, but when you heat the iron to a high enough temperature (called the Curie point), it loses its ability to be magnetized. Heat energy scrambles the iron atoms so that they can't line up and create a magnetic field. Here is a simple demonstration of this effect. 

 

• A small magnet. (Radio Shack's disk magnets work fine.)
• A stand to hold the magnet pendulum and wire. (The stand can be easily made from Tinkertoys™ or pieces of wood.)
• One 6-volt lantern battery (or other 6-volt power supply).
• 2 electrical lead wires with alligator clips at both ends (available at Radio Shack).
• One 3-inch (8 cm) length of thin iron wire, obtainable by separating one strand from braided picture-hanging wire.
• String, about 1 foot (30 cm) long.
• Adult help.

(15 minutes or less)

Make a stand from Tinkertoys™ or other wood as shown in the diagrams. Suspend the magnet from the top of the stand with a string. Make a pendulum at least 4 inches (10 cm) long. Stretch the iron wire between two posts so that, at its closest, the wire is 1 inch (2.5 cm) from the magnet.

(15 minutes or more) Touch the magnet to the iron wire. It 
should magnetically attract and stick to the wire.

Connect the clip leads to the terminals of the lantern battery. Connect one clip lead to one side of the iron wire, and touch the other clip lead to the iron wire on the opposite side of the magnet. Current will flow through the iron wire, causing the wire to heat up. (CAUTION: The wire will get hot!) As the iron heats up and begins to glow, the magnet will fall away from the wire. Take a clip lead away from the iron wire. Let the iron wire cool. When the iron wire is cool, notice that the magnet will stick to it once again.

If the wire does not heat up enough to glow red, move the clip leads closer together. 
 

The iron wire is made of atoms that act like tiny magnets, each one having a north and south pole of its own. These iron atoms usually point in all different directions, so the iron has no net magnetic field. But when you hold a magnet up to the iron, the magnet makes the iron atoms line up. These lined-up atomic magnets turn the iron into a magnet. The iron is then attracted to the original magnet.

High temperatures can disturb this process of magnetization. Thermal energy makes the iron atoms jiggle back and forth, disturbing their magnetic alignment. When the vibration of the atoms becomes too great, the atomic magnets do not line up as well, and the iron loses its magnetism. The temperature at which this occurs is called the Curie point

Inside the earth, there is a core of molten iron. This iron is at a temperature above the Curie point and therefore can't be magnetized. Yet the earth is magnetized, with a north and a south magnetic pole. The magnetic field of the earth comes from an electromagnet, that is, from electrical currents flowing inside the liquid metal core.

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Critical Angle - Why your phone calls don't leak out of optical fibers.

  

Critical Angle

 

Why your phone calls don't leak out of optical fibers.

A transparent material such as glass or water can actually reflect light better than any mirror. All you have to do is look at it from the proper angle. 

 

• A light source  with a well-defined beam. A laser is best, if one is available. Otherwise, you can use a Mini-Maglite� flashlight focused to make a beam, or a slide projector with its beam narrowed. (To narrow the beam of a slide projector, cut an index card the same size as a slide, and then make a hole in the middle of it with a paper holepunch. Put it in the projector so the light only goes through the hole.)
• A rectangular aquarium filled with water.
• A few drops of milk (or some powdered milk) to add to the aquarium water to make the beam visible.

(15 minutes or less)

Fill the aquarium with water. Then add the milk a drop at a time, stirring after each drop, until you can see the light beam pass through the water. If you use powdered milk, add a pinch at a time.

(15 minutes or more)

Direct the light beam upward through the water so that it hits the surface of the water from underneath. You can shine the beam into the water through the transparent bottom of the aquarium, or in through the side wall. (With the Mini-Maglite�, you can seal the light in a watertight plastic bag and place the light right in the water.) The beam will be more visible if you can dim the room lights.

Point the beam so that it hits the surface of the water at just about a right angle. In the aquarium, you may be able to see both the reflected beam, which bounces back into the water, and the refracted beam, which comes out of the water and into the air. (Dust in the air helps you see the refracted beam. You can add chalk dust to the air. You can also search for the beam and track it with a piece of paper.) Notice that most of the beam leaves the water and only a faint beam is reflected back down into the water.

Slowly change the angle at which the beam of light hits the surface of the water. Notice that the beam reflected into the water grows brighter as the beam transmitted into the air becomes dimmer. Also notice that the transmitted beam is bent, or refracted. 

Experiment until you find the angle at which the transmitted beam completely disappears. At this angle, called the critical angle, all of the light is reflected back into the water.  
 

In general, when a beam of light (the incident beam) hits the interface between two transparent materials, such as air and water, part of the beam is reflected and part of it continues through the interface and on into the other material. The light beam is bent, or refracted, as it passes from one material into the next. 

When the angles marked are greater than 49°, light is totally reflected from a water-air surface.	When the angles marked are less than 49°, some light leaves the water.

The farther the beam is from perpendicular when it hits the surface, the more strongly it is bent. If the light is moving from a material with a low speed of light into a material with a higher speed of light (for example, from water into air), the bending is toward the surface. At some angle, the bending will be so strong that the refracted beam will be directed right along the surface; that is, none of it will get out into the air. 

Beyond that angle (the critical angle), all the light is reflected back into the water, so the reflected beam is as bright as the incident beam. This phenomenon is called total internal reflection, because very nearly 100% of the beam is reflected, which is better than the very best mirror surfaces. 

The critical angle for water is measured between the beam and a line perpendicular to the surface, and is 49 degrees. 

Total internal reflection helps transmit telephone messages along optical fibers. Any light that is not aligned parallel to the axis of the fiber hits the wall of the fiber and is reflected (totally!) back inward,since the angle of incidence with which the light hits the wall is much larger than the critical angle. This helps prevent the signal from weakening too rapidly over long distances, or from leaking out when the fiber goes around a curve. This demonstration can also be done by replacing the aquarium and water with a small transparent plastic block, which can be bought at a local plastics supply store. Such blocks are also available as part of the Blackboard Optics� set made by Klinger Scientific.

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